**Answer:**

**your answer will be 699.78 km**

**Step-by-step explanation:**

I need help with my math homework

**Answer: Work shown below. Have a nice day! :)**

pls help

A. G

B. H

C. The functions have the same y-intercept.

**Answer:**

A.) G

**Step-by-step explanation:**

I'd say A.) G because when you look at the graph the y-intercept is 4. When you look at the equation the y-intercept is 6. 6 is bigger than 4 so then the answer should be A.) G

American children watch an average of 25 hours of television per week with a standard deviation of 8 hours. A random sample of 40 children is selected. What is the probability the mean number of hours of television they watch per week is less than 22? Question 15 options: 1) 0.3520 2) 0.0089 3) 0.9911 4) 0.6480

If **American **children watch an average of 25 hours of television per week with a standard deviation of 8 hours. the **probability **the mean number of hours of television they watch per week is less than 22 is: **2**) 0.0089.

First step is to find the **standard **deviation

σ = 8/√40

σ = 1.2649

Using this formula to find the **Z-**score

Z = x - μ/σ

Z =22-25/1.2649

Z = -3//1.2649

Z = -2.37

Hence,

P-value=P(Z < -2.37)

P-value =0.0089

Therefore the correct option is **2.**

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what are the coordinates of the point 3/5 of the way from A(3,-4) to B(13, 11)?

13-3 = 10. 10 times 3/5 = 6. 3+6 = 7 = the x coordinate of the point 3/5 from A to B

11+4 = 15. 15 times 3/5 = 9. -4+9 = 5 = the y coordinate of the point 3/5 from A to B

(7,5) is the point

11+4 = 15. 15 times 3/5 = 9. -4+9 = 5 = the y coordinate of the point 3/5 from A to B

(7,5) is the point

1/4+1/6 in fractions

Please help me I’m giving you 25 pints things

Write common denominator

3+2/12

Answer: 5/12

3+2/12

Answer: 5/12

5/12

Step by step:

1)Find the LCM of 6 and 4 =12

2)set both fractions to over 12 and do whatever you done to the bottom to the top

3)1x3=3 1x2=2

4)3+2 =5

Answer: 5/12

Step by step:

1)Find the LCM of 6 and 4 =12

2)set both fractions to over 12 and do whatever you done to the bottom to the top

3)1x3=3 1x2=2

4)3+2 =5

Answer: 5/12

Yes, by ASA and AAS

yes SAS

Yes by HL

yes by SSS

the two triangles are not congruent

**Answer:**

yes, by ASA

**Step-by-step explanation:**

sum of interior angles of a triangle = 180°

180 - (45+63) = 180 - 108 = 72°

the two triangles have two congruent angles and the side between them.

They are congruent for (ASA) angle side angle

The graph of linear function k passes through the points (-7, 0) and (1, 8).

Domain

2

Range

Slope

Y-intercept

X-intercept

The** linear function **is y = x + 7 and it has it **domain **and range at (-∞, ∞) respectively while it x and y - intercepts are (-7, 0) and (0, 7) respectively.

A** linear function** has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

The linear function always model the form of y = mx + c

m = slopec = y-interceptTaking the points, we can find the slope of the line

m = y₂ - y₁ / x₂ - x₁

m = 8 - 0 / 1 - (-7)

m = 8 / 8

m = 1

The slope of the line is 1

Using the slope to find the y - intercept;

y = mx + c

8 = 1(1) + c

8 = 1 + c

c = 8 - 1

c = 7

The** linear function** is y = x + 7

The **range **of this function is (-∞, ∞) and the **domain** of the function is

(-∞, ∞).

The x and y -intercept of the function are

x - intercept = (-7, 0)

y - intercept = (0, 7)

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A student is to be selected randomly from a group of students. For each classification of freshman and sophomore, there is a math major, an art major, and a biology major. The probability of each individual being selected is given in the following table:

Find the probability that

(a) a freshman is selected.

(b) an art major is chosen.

(c) a freshman math major or a sophomore biology major is chosen.

A freshman has a 0.35 chance of being chosen. A freshman has a 0.38 chance of being **chosen**. The **likelihood** of a freshman being chosen is 0.23.

A **probability** is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as **percentages** ranging from 0% to 100%. It is predicated on the likelihood of something occurring. The rationale underlying probability is the foundation of **theoretical** probability. If a coin is tossed, the theoretical probability of receiving a head is 12.

Here,

.................. Math .. Art . Biology Total

Freshman . 0.10 . 0.08 . 0.17 .... 0.35

Sophomore 0.22 . 0.30 . 0.13 ... 0.65

Total ......... 0.32 . 0.38 . 0.30 ...... 1

(a) 0.35

(b) 0.38

(c) 0.10 + 0.13 = 0.23

The **probability** that a freshman is selected is 0.35. The probability that a freshman is selected is 0.38. The probability that a freshman is **selected** is 0.23.

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What is the solution and how do I solve?

20 + 4x+2 = 6x+8 --- By exterior angle

4x+22=6x+8

4x-6x=8-22

-2x=-14

x=7

Hope it helps

20 + 4x+2 = 6x+8

22 + 4x = 6x+8

4x-6x = 8-22

-2x = -14

x=7

Answer: x=7

22 + 4x = 6x+8

4x-6x = 8-22

-2x = -14

x=7

Answer: x=7

coordinate plane notes pratice

help pleaseeee tyyyvm :)

The **graph **in which point are plotted is given below and Point D and F lie on Y axis and X axis respectively other lie on the different **quadrant **

**What does a math quadrant mean?**

The term "**quadrant**" refers to each of the four divisions of the **coordinate **plane. Furthermore, when we speak of the sections, we also mean the sections as the **coordinate **axes split them. This is where the x-axis is, and this is where the y-axis is on the up-down axis. On a **coordinate **plane, it divides the space into four parts, as you can see.

Point A (-5,4)

Lies in 2 **quadrant **of the **graph**

Point B (-3,-2)

Lies in 3 **quadrant **of the **graph**

Point C (4,6)

Lies in 1 **quadrant **of the **graph**

Point D (0,-4)

Lies on negative y axis of the **graph**

Point E (2,-1)

Lies in 4 **quadrant **of the **graph**

Point F (1,0)

Lies on positive x axis of the **graph**

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-15x + 20y = 15

0=18x + 24y - 18

**Answer:**

**Step-by-step explanation:**

given:

-15x + 20y =15

0 = 18x + 24y -18

let's get the 2nd equation into a form like the top equation

-18x -24y = -18

multipy thur by -1

18x +24y = 18

we'll need to use substitution for this problem. elimination has a zero issue.

18x = -24y +18

x = -[tex]\frac{4}{3}[/tex] y + 1

now plug this into the 1st equation

-15( -[tex]\frac{4}{3}[/tex] y + 1 ) + 20 y = 15

20y -15 +20y = 15

40y = 30

y = 3/4

now that we've found y, plug that into our x = -[tex]\frac{4}{3}[/tex] y + 1 , to find x

x = -1 +1

x = 0

One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer

One factor of the **function **f(x) = x3 − 6x2 + 11x − 6 is (x − 3). the x-intercepts and the y-intercept of the graph of f(x) are

Generally, To find the** x-intercepts**, we set y equal to 0 and solve for x. In this case, the equation we need to solve is:

f(x) = x^3 - 6x^2 + 11x - 6 = 0

To solve this equation, we can use the fact that (x - 3) is a factor of the function. This means that we can write the function as:

f(x) = (x - 3)(x^2 - 3x + 2)

If (x - 3) is a factor, then x - 3 must equal 0. This gives us one x-intercept at x = 3.

To find the other x-intercepts, we can set the quadratic factor (x^2 - 3x + 2) equal to 0 and solve for x. This gives us the following equation:

x^2 - 3x + 2 = 0

We can use the quadratic formula to solve this equation:

x = (3 +/- √(9 - 8)) / 2 = (3 +/- √(1)) / 2 = (3 +/- 1) / 2

This gives us two more** x-intercep**ts at x = 2 and x = 4.

So the** x-intercepts** of the graph of f(x) are x = 2, x = 3, and x = 4.

To find th**e y-intercept,** we set x equal to 0 and solve for y. In this case, the equation we need to solve is:

f(0) = 0^3 - 6(0)^2 + 11(0) - 6 = -6

This gives us a y-intercept at (0, -6).

So th**e y-intercept** of the graph of f(x) is (0, -6).

All of the intercepts of the graph of f(x) are, therefore (0, -6), (2, 0), (3, 0), and (4, 0).

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2^3 + (-16) / 4^2 x 5 - (-3)

-8/83 (see attatched image for work)

Solve for m in the equation below. It may be helpful to convert the equation into exponential form. Write answer as an integer or reduced fraction. -2. log,(m) - 24 = - 20 m = > Next Question Find the largest value of 2 that satisfies: log, () – log (2 + 1) = 9 =

The largest **possible** value of 2 that **satisfies** the **equation** is **approximately** **1.1**.

**What is Exponential Form Equation?**

Since **y=bx, **y = b x is a one-to-one **inverse** of the **exponential** function, x=by x = b y, it too is a **function**. We simply **swap** x and y and solve for y to **discover** the **inverse function**, as is the case with all **inverse** **functions**.

To solve for m in the **equation** -2 * log(m) - 24 = -20, we can start by **converting** the **equation** into **exponential** **form**. To do this, we can raise both **sides** of the **equation** to the **power** of **e**:

[tex]e^(-2 * log(m) - 24) = e^(-20)[/tex]

Then we can simplify:

[tex]m^(-2) = e^(-20)[/tex]

Then we can solve for m:

[tex]m = sqrt[e^20]\\\\= sqrt[20*e^9]\\\\= sqrt[20] * sqrt[e^9]\\\\= 2 * 3^(1/2)= 2 * 1.732\\\\= 3.464[/tex]

So **m** is **approximately** equal to 3.464

To find the **largest** value of 2 that **satisfies** the **equation** [tex]log(2^2) - log(2 + 1) = 9[/tex], we can start by **expanding** the **left-hand side** of the equation:

[tex]log(2^2) - log(2 + 1) \\\\=log(2^2 / (2 + 1))\\\\ = log(4/3) = 9[/tex]

Then we can rewrite the **equation** as:

log(4/3) = 9

Then we can solve for 2:

[tex]2 = (4/3)^(1/9)\\\\= (4^(1/9)) / 3^(1/9)\\\\= 1.5874010519681994 / 1.4422495703074083\\\\= 1.1[/tex]

So, The largest **possible** value of 2 that **satisfies** the **equation** is **approximately** **1.1**.

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For Christmas you want to get your parents a framed family picture. At the framing store, there are 4 different styles each available in 5 different colors. You decide to use a blue mat board and there are 3 different shades of blue to choose from. How many different frames can you create?

The **number **of different frames you can create, if There are 4 different styles, each available in 5 different **colors**, there are 3 different **shades **of blue to choose from, is 12.

A **combination **is a choice of items from a group of **different **items, where the order of the choices is **irrelevant**.

**Given**:

There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from,

Calculate the total number of frames, we can create as shown below,

The number of frames = different styles available for blue color × shades of blue

The number of frames = 4 × 3

The number of frames = 12

Thus, the number of frames you can create is 12.

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In an adjacency ____ representation, corresponding to each vertex v is a linked list such that each node of the linked list contains the vertex u, and there is an edge from v to u.

In an adjacency **list **representation, corresponding to each vertex v is a linked list such that each node of the **linked list** contains the vertex u, and there is an edge from v to u.

This is a common way to represent a **graph **in **computer **memory, where each **vertex **is represented by an object that stores its adjacent vertices in a list. This representation is useful when the graph is sparse, meaning it has relatively few **edges **compared to the number of vertices it has. It is not as efficient for dense graphs, where the number of edges is close to the **maximum **possible number of edges.

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For the function f(x) x 9, find (f f 1)(5)

the **value **of [tex]f o f^{-1}[/tex](5) of the** function **f(x) = x + 9 is 5

An** inverse function** or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f^-1 or F^-1. One should not confuse (-1) with** exponent** or **reciprocal **here.

[tex]f^{-1}[/tex](x) =

if f(x) = x + 9

setting x + 9 = y and making x the** subject** we have

y = x + 9

x = y - 9

replacing x with [tex]f^{-1}[/tex](x) and y with x we have

[tex]f^{-1}[/tex](x) = x - 9

so the f o [tex]f^{-1}[/tex](x) can be gotten by substituting x in f(x) with x - 9 so that we have

f o [tex]f^{-1}[/tex](x) = (x - 9) + 9

f o [tex]f^{-1}[/tex](x) = x

so f o [tex]f^{-1}[/tex](5) will be x = 5

which becomes

f o [tex]f^{-1}[/tex](5) = 5

In conclusion f o [tex]f^{-1}[/tex](x) is 5

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Caroline went to the grocery store and bought bottles of soda and bottles of juice.

Each bottle of soda has 30 grams of sugar and each bottle of juice has 15 grams of sugar. Caroline purchased a total of 6 bottles of juice and soda which collectively contain 150 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased, ∞, and the number of bottles of juice purchased, y.

The **solution** of the **system of equations** is the point of intersection (4, 2), as shown in the **graph** below.

Caroline bought 4 soda bottles.

Caroline bought 2 juice bottles.

How to Solve a System of Equations?In order to determine the solution to this problem, use the information given to create two **equations**.

Number of soda bottle = x.

Number of juice bottle = y.

First **Equation **for the total number of bottle that Kelvin bought

x + y = 6 --> eqn. 1

Second **Equation **2 for the total sugar in the soda bottles and total sugar in juice bottles that equals 150 grams of sugar.

30x + 15y = 150

Simplify by dividing by 5

6x + 3y = 30 --> eqn. 2

Rewrite eqn. 1:

y = 6 - x

Solve simultaneously for the variables of x and y, by substituting the value of y into **equation **2:

6x + 3(6 - x) = 30

6x + 18 - 3x = 30

3x + 18 = 30

3x = 30 - 18

3x = 12

3x/3 = 12/3

x = 4

Caroline bought 4 soda bottles.

Substitute x = 4 into **equation** 1 to find the value of y:

x + y = 6

4 + y = 6

y = 6 - 4

y = 2

Caroline bought 2 juice bottles.

The **graph** below shows the point of intersection, (4, 2), which is the solution.

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On May 26, your balance is $897.96. On May 27, you write check #117 to your landlord, Mrs. Wall, for $366.00. On May 28, you use receive a rebate check for $62.52. On May 29, you write a check for $137.32 to Bank of America for your car payment. On May 30, you receive your monthly check from your employee of $658.50 On May 31, you write a check for $685 to your parents for supporting you the previous month. What is the ending balance for the month of May?

**Bank reconciliation** is an accounting process to bring the balance as per the bank statement to agree with the balance as per the checkbook.

The **journal entry **to adjust the checkbook balance is as follows:

May 1 Debit Bank Charges $20

Credit Checkbook $20

The preparation of the Bank Reconciliation Statement is as follows:

Balance as per bank statement $16,833.19

Add Uncleared Deposits $1,650.00

Less Outstanding Checks $2,040.84

Balance as per adjusted checkbook $16,442.35

Checkbook balance on May 31 = $16,462.35

Bank Statement balance on May 31 = $16,833.19

Uncleared Deposits:

May 29 $575

May 30 $1,075 $1,650

Outstanding Checks:

Check 189 - $127.50

Check 191 - $462.19

Check 192 - $569.42

Check 194 - $881.73 $2,040.84

Bank charges = $20.00

**Checkbook Adjustment:**

Balance as per checkbook $16,462.35

Less Bank charges 20.00

Adjusted checkbook balance $16,442.35

Transaction Analysis for Journal:

Bank Charges $20 Checkbook $20

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Dajon already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 15 years

in an account paying 2.05% interest, how much could the annuity provide each week? Round your answer to

the nearest dollar.

The **annuity** provide each **week** is $547.59 (approx.)

**Define Annuity**

A **fixed** sum of money paid to someone **each** year, typically for the rest of their life.

Given,

Dajon already **knows** that he will **have** $500,000 when he retires.

P = $500,000

Next, he sets up a **payout** **annuity** for 15 **years** in an account paying 2.05% **interest**.

r = 2.05 % or 0.0205

t = 15 **years**

Since, **annuity** provide **each** week then

n = 52 **weeks** (in a year)

The **Annuity** formula is,

**P = d [ ( 1 + r/n)^nt - 1 ] / (r/n)**

where, d = regular **deposit**

Now, plug in the **values** and find the **value** of d

P = d [ ( 1 + 0.0205/52)^52*15 - 1 ] / (0.0205/52)

**Calculate** the value it gives,

**P = $547.5936993 or 547.59 **

Hence, the **annuity** provide **each** week is $547.59 (approx.)

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What are the solutions to this system? Select all that apply. Y+2x^2 =14

y= 3x^2-6

The s**olution** to the** system of equation** y + 2x² = 14 , y = 3x² - 6 is as follows:

**System of equation** can be solved using different method such as elimination method, substitution method and graphical method.

Let's solve the system of equation by** substitution method**.

Therefore,

y + 2x² = 14

y = 3x² - 6

Therefore, using substitution method,

3x² - 6 + 2x² = 14

5x² - 6 = 14

5x² = 14 + 6

5x² = 20

x² = 20 / 5

x² = 4

x = √4

x = 2

Therefore, let's find the value of y using y = 3x² - 6.

y = 3x² - 6

y = 3(2)² - 6

y = 12 - 6

y = 6

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a small bookshelf is 8/12 yard long. How many books can fit on the shelf if the width of each book is 1/24 yard? Explain

Answer:

16 books

Step-by-step explanation:

8/12 is equivalent to 16/24. If each book is 1/24 width, 16/1 = 16

r²-6 r+9 can be factorized to give an expression of the form (r+a)²,

where a is an integer.

Work out the value of a.

The **value **of a in the **expression **is -3

From the question, we have the following parameters that can be used in our computation:

r²-6 r+9 can be **factorized **to give an **expression** of the form (r+a)²

This means that

r² - 6r + 9 = (r+a)²

**Factorize **the expression r² - 6r + 9

So, we have

(r - 3)² = (r + a)²

By comparison, we have

a = -3

Hence, the solution of a is -3

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A cake recipe asks for 1/4 cup of oil for each cake. How many cakes can be made from a bottle of oil that has 4 cups in it?

**Answer: 16**

**Step-by-step explanation:**

there are 4 1/4 in 1 cup. so it'll be 4 cakes for each cup of oil you have. multiply the number of cakes that can be made per cup (4) by the number of cups you have (4)

(4) x (4) = 16

Work out the surface area of this solid

prism.

10cm

8cm

27cm

6cm

17cm

30cm

The diagram is not drawn to scale.

**Answer:**

2064 cm²

**Step-by-step explanation:**

You want the **surface area of a prism** that is **30 cm between bases** that are **trapezoids** with parallel sides **27 cm and 6 cm** that are **8 cm** apart, and** slant sides** that are **10 cm and 17 cm**.

The area of each trapezoidal base is ...

A = 1/2(b1 +b2)h

There are two **identical bases**, so their **total area** is ...

2A = (b1 +b2)h = (27 cm +6 cm)(8 cm) = **264 cm²**

The lateral area of the prism is the area of the four rectangular faces. Each is 30 cm wide, and their total length is the perimeter of the base;

P = 27 cm +10 cm +6 cm +17 cm = 60 cm

**lateral area =** Ph = (60 cm)(30 cm) **= 1800 cm²**

Total surface area

The total surface area of the prism is the sum of the base area and the lateral area:

total area = base area + lateral area

total area = 264 cm² +1800 cm² = **2064 cm²**

**The surface area of the solid prism is 2064 cm²**.

work out the area of a rectangle with base, b = 9.6mm and hight, h = 2mm

**Answer: 19.2mm^2**

**Step-by-step explanation: the area of a rectangle is simply base x height**

**so do 9.6 x 2 to get 19.2mm^2**

A student receives a subsidized student loan for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments. Find her monthly payment and total interest paid if the interest rate is 5.5%.

If the **interest** **rate** is 5%, the monthly payment and total interest would be $2.439.

**Interest** is the sum of money that must be repaid on a loan or received in exchange for a loan. Principal refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.

Given,

A student receives a subsidized student **loan** for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments.

A $10,000 subsidized student loan

Ten-year term of repayment

5.5% interest rate

First, we must determine the loan's **future** **value** (FV) over the next six months using the formula below:

FV in 6 months

= Loan Amount× (1 + Interest Rate)⁶ ($10,000×(1 + 0.055) ×6

= $2.7680.

Second, the formula for determining future value is used to determine the **monthly** **payment**:

M = FV in 6 months / (((((r)n) - 1) / r).......... (1)

When you enter all the pertinent values into equation (1), you get:

M = $2.7680 / ((((1 + 0.00466666666666667)^144) – 1) / 0.00466666666666667)

M = $2.439

Therefore, if the **interest** rate is 5.5%, the total amount paid in interest plus monthly payments would be $2.439.

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Can someone evaluate these for me

1×(– 6 × –18 –8) ÷4

4– – 20+ – 5 ×( –11 – –18)

13– – 10 × 16 ÷ (14 + –16)

1– – 9 × 12 ×(–19 +20)

The answer of the given expression using **BODMAD rule** is **25**.

**What is BODMAS rule?**

The **BODMAS rule** states that the brackets must be solved first, then powers or roots (i.e., of), **Division**, **Multiplication**, **Addition**, and finally **Subtraction**. Only when the **BODMAS rule** or the **PEDMAS rule** is used to solve an expression is the **solution** deemed to be correct.

**(a)** 1 x (-6 x -18 - 8) ÷ 4

By using first to simplify the bracket.

1 x ((-6 x -18) - 8) ÷ 4

1 x (108 - 8) ÷ 4

(1 x 100) ÷ 4

100 ÷ 4

25

Hence, the answer of the given expression using **BODMAD rule** is **25**.

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Which of the following statements regarding the expansion of (x + y)^n are

correct?

A. The coefficients of x-1 and y- 1 both equal 1.

B. For any term xay in the expansion, a - b = n.

C. The coefficients of x and y both equal 1.

D. For any term xay in the expansion, a + b = n

The** true statements **are,

A. The coefficients of xⁿ and yⁿ both equal 1.

D. For any term x and y in the expansion, a + b = n

**What is an expression?**

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The **expression **is,

⇒ (x + y)ⁿ

Now,

We know that;

A binomial expansion is,

⇒ [tex](x + y)^n = x^n + nx^n^-^1 y + ^{n} C_{2} x^n^-^2y^2 + ..... + nxy^n^-^1 + y^n[/tex]

Clearly, **For Option A: **

The coefficients of xⁿ and yⁿ both equal 1.

If we see first and last term of the expansion, This statement is true.

For **Option D:**

For any term xᵃyᵇ in the expansion, a + b = n.

Let we take 3rd term of expansion

Here, a = n-2 and b=2

So, a + b = n-2+2 = n

Thus, a + b = n is true statement.

**For Option B: **

For any term xᵃyᵇ in the expansion, a - b = n.

Let we take 3rd term of expansion

Here, a=n-2 and b=2

If we do a-b = n-2-2=n-4≠n

Thus, a-b=n is false statement.

Thus, The** true statements **are given below,

A. The coefficients of xⁿ and yⁿ both equal 1.

D. For any term x and y in the expansion, a + b = n

Learn more about** the mathematical expression **visit:

brainly.com/question/1859113

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Which of the following is a true statement? A. All real numbers are rational numbers. B. All whole numbers are natural numbers. C. All integers are whole numbers. D. All natural numbers are integers.

**Answer: It is D**

**Step-by-step explanation:**

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